# Symmetric difference

This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
Find a ven diagram and make an infobox
This page requires references, it is on a to-do list for being expanded with them.
Please note that this does not mean the content is unreliable, it just means that the author of the page doesn't have a book to hand, or remember the book to find it, which would have been a suitable reference.

## Definition

Let [ilmath]A,B\in\mathcal{P}(X)[/ilmath] be two subsets of a set [ilmath]X[/ilmath]. We define the symmetric difference of [ilmath]A[/ilmath] and [ilmath]B[/ilmath] as:

• [ilmath]A\triangle B:=(A-B)\cup(B-A)[/ilmath][Note 1]
• In words: [ilmath]A\triangle B[/ilmath] contains (everything in [ilmath]A[/ilmath] and not in [ilmath]B[/ilmath]) and (everything in [ilmath]B[/ilmath] but not in [ilmath]A[/ilmath]).

Claim 1: this is equivalent to [ilmath]A\triangle B:=(A\cap B^C)\cup(A^C\cap B)[/ilmath]